Jul 7, 2016 · int 9/x^3 d x=-9/(2x^2)+C int 9/x^3 d x int 9/x^3 d x=9 int (d x)/x^3 int 9/x^3 d x=9 int x^(-3) d x "now use power rule" int 9/x^3 d x=9 [1/(-3+1)x^(-3+1)] int 9/x^3 ...

Apr 2, 2017 · See the entire solution process below: The absolute value function takes any negative or positive term and transforms it to its positive form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent. -9 < x - 3 < 9 Add color(red)(3) to each segment of the system of inequalities to solve for …

Sep 25, 2015 · =color(blue)(3xsqrtx sqrt(9x^3) can be written as: sqrt(3^2 *color(blue)(x^2*x) =color(blue)(3 *x) sqrt x =color(blue)(3xsqrtx

May 5, 2017 · How do you find the volume of a prism if the width is x, height is #2x-1# and the length if #3x+4

Jun 18, 2018 · x = -10 Step 1, distribute the 3 and 9 into the parentheses: 3(2x-1) -> 6x-3 9(x+3) -> 9x+27 Step 2 ...

Dec 7, 2016 · Thus, f(x) is not continuous at x=3. Bonus: Here's a tip to determine where some functions will be discontinuous. Any x-value that makes any denominator in the function equal to 0 is a point of discontinuity. So for the function above, x-3=0 when x=3, and so the function will be discontinuous at x=3.

Aug 4, 2016 · 8sin^(-1)((x-3)/3) - sqrt(9-(x-3)^2) + C I hope you like substitutions, because we're about to do a lot of them. To start, let u = x-3 implies du = dx Integral becomes: int (u+8)/(sqrt(9-u^2)) du Now we want to deal with the denominator. This type of function will often involve a trig substitution - if you learn/can derive the pythagorean identities they are very helpful in …

Jan 25, 2017 · x ( 3x + 1 )( 3x-1 ) x is common to both terms, so you can take it out of both and put the other factor in a bracket. 9x^3 -x =x ( 9x^2 - 1). (x^2 -1) and similar expressions are known as the difference of two squares, and can be further factorised to give: x( 3x + 1 )( 3x - 1 ).

Sep 25, 2016 · (I am assuming that we want to stay in the real numbers.) As xrarr3^-, the numerator is approaching 6 and the denominator is a positive number approaching 0. As xrarr3^-, the ratio is increasing without bound. lim_(xrarr3^-) sqrt(x^2-9)/(x-3) = lim_(xrarr3^-) (x+3)/sqrt(x^2-9) =oo

Mar 24, 2017 · Labelling the equations. #color(red)(y)=4x-9to(1)# #color(red)(y)=x-3to(2)# Since both equations have y as the subject we can equate the right sides.